Captain Kane scored his second England hat-trick in a 4-0 rout of Bulgaria at Wembley Stadium on Saturday to leave Southgate's side top of qualifying Group A with nine points from three games.
The 26-year-old Tottenham Hotspur striker has now scored 25 goals in 40 appearances and moved ahead of 1966 World Cup final hero Geoff Hurst in the all-time England scoring list.
Sterling's pass allowed Kane to open the scoring after 24 minutes and he was repaid in the second half with Kane squaring for him to add his name to the scoresheet.
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Manchester City's Sterling, who once went 27 games for England without a goal over a three-year period, has now scored five in their three Euro 2020 qualifiers, including a hat-trick against the Czech Republic in March.
Kane and Sterling, two very different forwards, have scored 10 of England's 14 goals in the three qualifiers and Southgate was effusive in his praise for both.
"I thought that he was outstanding," Southgate said of Sterling. "He'll probably have the hump that he's only got one today because his mindset has shifted so much towards that desire to score goals.
"Two years ago when we were working with him, he was still a dangerous player, but he just didn't have that same desire to get into those areas and that ruthlessness in front of goal."
Kane's two clinically-struck penalties means he has scored eight from the spot for England, one behind the record of Frank Lampard. It is a skill Southgate says should be admired.
"We stood and watched him take penalties for about 20 minutes yesterday," he said. "When you watch the process that he goes through, he just gives himself every chance of succeeding by that deliberate practice.
"If you can be confident on the bench when a penalty is given, we're as confident as we possibly could be.

Harry Kane trifft doppelt für England

Image credit: Getty Images

"You always know there's a chance that even the most outstanding penalty can be saved, but in those moments, he really has supreme temperament and technique."
Kane is the first player to score 25 or more goals in his first 40 appearances for England since Gary Lineker and is clearly thriving with Sterling alongside him.
"It's great for him that he's taken his club form into international form, he's an amazing player," Kane said.
"I managed to repay the favour (having set up Sterling's goal). We enjoy playing together, we all do."
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